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Introduction to Amplifiers The BJT is an an excellent amplifier when biased in the forward-active region. The FET can be used as an amplifier if operated in the saturation region. In these regions, the transistors can provide high voltage, current and power gains. DC bias is provided to stabilize the operating point in the desired operation region. The DC Q-point also determines –The small-signal parameters of the transistor –The voltage gain, input resistance, and output resistance –The maximum input and output signal amplitudes –The overall power consumption of the amplifier

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BJT Amplifier (continued) An 8 mV peak change in v BE gives a 5 A change in i B and a 0.5 mA change in i C. The 0.5 mA change in i C gives a 1.65 V change in v CE. If changes in operating currents and voltages are small enough, then I C and V CE waveforms are undistorted replicas of the input signal. A small voltage change at the base causes a large voltage change at the collector. The voltage gain is given by: The minus sign indicates a phase shift between input and output signals.

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A Practical BJT Amplifier using Coupling and Bypass Capacitors AC coupling through capacitors is used to inject an ac input signal and extract the ac output signal without disturbing the DC Q-point Capacitors provide negligible impedance at frequencies of interest and provide open circuits at dc. In a practical amplifier design, C 1 and C 3 are large coupling capacitors or dc blocking capacitors, their reactance (X C = |Z C | = 1/ C) at signal frequency is negligible. They are effective open circuits for the circuit when DC bias is considered. C 2 is a bypass capacitor. It provides a low impedance path for ac current from emitter to ground. It effectively removes R E (required for good Q-point stability) from the circuit when ac signals are considered.

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DC and AC Analysis -- Application of Superposition DC analysis: –Find the DC equivalent circuit by replacing all capacitors by open circuits and inductors (if any) by short circuits. –Find the DC Q-point from the equivalent circuit by using the appropriate large-signal transistor model. AC analysis: –Find the AC equivalent circuit by replacing all capacitors by short circuits, inductors (if any) by open circuits, dc voltage sources by ground connections and dc current sources by open circuits. –Replace the transistor by its small-signal model (to be developed). –Use this equivalent circuit to analyze the AC characteristics of the amplifier. –Combine the results of dc and ac analysis (superposition) to yield the total voltages and currents in the circuit.

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DC Equivalent for the BJT Amplifier All capacitors in the original amplifier circuit are replaced by open circuits, disconnecting v I, R I, and R 3 from the circuit and leaving R E intact. The the transistor Q will be replaced by its DC model. DC Equivalent Circuit

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AC Equivalent for the BJT Amplifier The coupling and bypass capacitors are replaced by short circuits. The DC voltage supplies are replaced with short circuits, which in this case connect to ground.

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AC Equivalent for the BJT Amplifier (continued) By combining parallel resistors into equivalent R B and R, the equivalent AC circuit above is constructed. Here, the transistor will be replaced by its equivalent small-signal AC model (to be developed).

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Hybrid-Pi Small-signal AC Model for the BJT The hybrid-pi small-signal model is the intrinsic low- frequency representation of the BJT. The small-signal parameters are controlled by the Q-point and are independent of the geometry of the BJT. Transconductance: Input resistance: Output resistance:

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Small-signal Current Gain and Amplification Factor of the BJT o > F for i C I M, however, o and F are usually assumed to be about equal. The amplification factor is given by: For V CE << V A, F represents the maximum voltage gain an individual BJT can provide, independent of the operating point.

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Example o Calculation for 2N2222A Choose the Q-point at about (5 V, 5 mA) for this analysis. Notice the slope of the DC current gain characteristic in this region. Ideally, the slope would be zero.

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at about I C = 5 mA and 25 °C for F = 180 Given the tolerances usually encountered in forward current gain, the assumption of F = o seems reasonable for preliminary analysis and initial designs. From Figure 3 for the 2N2222A BJT at the chosen Q-point…

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Equivalent Forms of the Small-signal Model for the BJT The voltage-controlled current source g m v be can be transformed into a current-controlled current source, The basic relationship i c = i b is useful in both dc and ac analysis when the BJT is biased in the forward-active region.

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Small Signal Operation of BJT For linearity, i c should be directly proportional to v be. If we limit v be to 5 mV, the relative change in i c compared to I C that corresponds to small-signal operation is: for

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Small-Signal Analysis of the Complete C-E Amplifier: AC Equivalent The AC equivalent circuit is constructed by assuming that all capacitances have zero impedance at signal frequency and the AC voltage source is at ground. Assume that the DC Q-point has already been calculated.

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Capacitor Selection for the CE Amplifier The key objective in design is to make the capacitive reactance much smaller at the operating frequency f than the associated resistance that must be coupled or bypassed.

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C-E Amplifier Input Resistance The input resistance, the total resistance looking into the amplifier at coupling capacitor C 1, represents the total resistance presented to the AC source.

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C-E Amplifier Output Resistance The output resistance is the total equivalent resistance looking into the output of the amplifier at coupling capacitor C 3. The input source is set to 0 and a test source is applied at the output. But v BE =0. since r o is usually >> R C.